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Color digital cameras are typically implemented by putting a color filter array (CFA) like a Bayer filter, plus an infrared cut filter, in front of a sensor that is sensitive to light frequencies spanning the full visible spectrum plus some range to either side of it.

The filters have two degradative effects:

  1. They exclude light from reaching the sensor. (E.g., a "green" sensor pixel may only receive photons that are within the range 500-570nm. Most others are rejected.)

  2. Resolution is lost to "mosaic" effects. (E.g., a green image component is only seen by half of the pixels in a Bayer filter.)

How are these losses quantified, and what is their typical magnitude in practice?

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The idea that any particular wavelength is only allowed to pass through one particular color of the three colors used in a Bayer masked filter has been perpetuated to death. Fortunately, it is false.

Here's a typical enough spectral response curve of a specific camera sensor.
Sony IMX249 absolute QE
The visible (to humans) spectrum ranges from 390 to 700 nanometers. Notice that the "green" pixels respond, to one degree or another, to the entire range of visible light. That response is greatest between about 500 and 570 nanometers, but it is by no means zero at other wavelengths. The same is true of the "red" and "blue" filters. Each allows some light from the entire visible spectrum to pass. What differentiates them is in just how much of the light of a particular wavelength is allowed to pass through and how much is reflected or absorbed.

There are Bayer masked CMOS sensors in current DSLRs that have quantum efficiencies approaching 60%. That should be enough to eliminate the fallacy that only 1/3 of visible light that falls on a Bayer masked sensor is allowed to pass the filter and be measured by the pixel wells. If that were indeed fact then the highest quantum efficiency of a Bayer masked filter would be limited to 33%.

Note that the human response to visible light is similar. The cones in our retinas also overlap significantly in their spectral response.
human spectral response

What we perceive as colors are the differences in the way our brains process the varying response of of our blue, green, and red cones to different wavelengths and combinations of wavelengths.

In theory the infrared cut filter doesn't reduce any light visible to human vision because none of the light it prevents from reaching the sensor is visible to human eyes. Infrared, by definition, begins just outside the range of visible light at 700 nanometers and extends wavelengths of 1,000,000 nanometers (1 mm). Digital sensors are typically sensitive to IR light from between 700 and 1,000 nanometers. In practice sometimes the near-infrared wavelengths just under 700 nanometers are attenuated slightly by the IR-cut filters.

So just how bad are the "degradative effects" identified in the question?

They exclude light from reaching the sensor. (E.g., a "green" sensor pixel may only receive photons that are within the range 500-570nm. Most others are rejected.)

As covered above, the best current CMOS sensors in DSLRs and other cameras have quantum efficiencies in the visible spectrum ranging from between 50-60%. In one sense you could say they lose roughly half the light that falls on them, or one photographic stop. But that's not a whole lot different than the human retina so the argument could be made that they don't lose much of anything compared to what we see with our eyes.

Resolution is lost to "mosaic" effects. (E.g., a green image component is only seen by half of the pixels in a Bayer filter.)

Again, all three colors in a typical Bayer array are sensitive to at least some of the "green" wavelengths between 500-570 nanometers. This overlap is leveraged when the monochromatic luminance values from each pixel well are demosaiced to create R, G, and B values for each pixel on the sensor. It turns out that in terms of the ability to resolve alternating black and white lines a Bayer masked sensor has absolute resolution that is about 1/√2 of a non-masked monochromatic sensor of the same pixel pitch.

  • The first graph is not insightful because, really, only a fraction of colour filters would have the QE of a channel. Divide blue, red graphs by 4 and green graph by 2, sum them and you will see that resulting QE graph (which is roughly equal to what you get if you use monochrome conversion in post) is magnitude smaller than monochrome QE. it does show that Bayer CFAs are not loosing much more than what they are expected to by design though. – Euri Pinhollow Mar 2 '17 at 8:00
  • The QEs quoted are measured with the Bayer mask in place. – Michael C Mar 2 '17 at 9:19
  • How was monochrome QE obtained then? – Euri Pinhollow Mar 2 '17 at 9:33
  • I haven't quoted anything regarding monochrome QE. I referenced monochrome resolution limits. – Michael C Mar 2 '17 at 9:43
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    @feetwet practically Bayer CFA does not cut resolution of monochrome objects given that they are not too saturated. 50% of QE cut is optimistic, it may be well less than that. – Euri Pinhollow Mar 2 '17 at 18:44
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There's no "lost" resolution. A manufacturer may engage in "specmanship" by advertising X-megapixels, but the resolution is defined by the pixel size, fill factor (what percent of the pixel surface is light-sensitive), and the number of pixels per color group. Further, there are well-developed algorithms for 'retrieving' resolution within an RGBG group based on a posteriori analysis of the RGBG group's, and its neighboring pixels', signals.

As to filter thruput: the spectral transmission curves for common camera RGB (and RGBY for some esoteric designs) are readily available on the web. Use them with care, since the signal loss for a given photopic (retina + brain) color, typically caused by several different incoming photon wavelengths, can vary considerably from one color to another. However, camera manufacturers are well aware of this, so both the RAW lookup tables and the internal JPG converters perform a color-rebalancing algorithm to compensate.

  • Regarding the resolution: I think what you're saying is that advertised resolution for a color sensor is largely tied to the number of Bayer groups. I.e., it is more than 1 pixel per Bayer group, but it's definitely not 4 pixels per Bayer group. But note that with no Bayer filter you really do get 4 pixels where before you had 1 Bayer group. – feetwet Mar 1 '17 at 17:12
  • "but the resolution is defined by ... the number of pixels per color group" - I think that it is reasonable to at least mention that resolution can be both chromatic and luminous. I.e. Xtrans cameras have bigger share of green pixels and they have better luminous resolution but worse chromatic resolution. – Euri Pinhollow Mar 2 '17 at 12:26
  • @EuriPinhollow You make a good point, but I'd suggest not using "resolution" to describe chromatic accuracy. That's nonstandard usage. – Carl Witthoft Mar 2 '17 at 12:27
  • @CarlWitthoft I did not say anything about chromatic accuracy (Luther Ives conditions are completely different story). White, red, green, blue objects will be rendered with different details depending on CFA. Xtrans will give somewhat better resolution for white and green objects than bayer sensor but will resolve red and blue objects somewhat worse. This is what I mean when I say that Xtrans have worse chromatic resolution. Foveon X3 sensor will not favour any colour at all (in well lit conditions, aggressive colour transformation is not considered). – Euri Pinhollow Mar 2 '17 at 12:33
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Summarizing from comments here, an upper bound on light loss due to an RGB filter is indeed a factor of 3, or 1.6 stops. In reality the response of each color filter element has some spectral overlap, so it's not quite that severe. Matt Grum estimates a factor of 2.5, or 1.3 stops.

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